To me, the biggest issue here is that, while "the condensation would be only on the inside of the pipe", you are in fact anticipating condensation, which can lead to mold, in the pipe. And if you're blowing air through the pipe, you could be creating a mold nursery in the pipe that significantly increases the amount of mold spores in the air, and then mold elsewhere in the house.
You've mentioned that "I cannot keep the door closed, so your average "single room" humidifier doesn't move the needle". If I understand your proposal correctly, you plan to address this concern by pump so much humidity into the room that even with normal airflow in the house removing humidity, that room will stay at the humidity you want. But that means you are going to be pushing a very large amount of moisture into the rest of the house.
Your post implies that the humidity in the rest of the house is fine, which means that if you start adding a large amount of moisture to it, it will become "not fine". So you may also wind up creating a mold problem elsewhere in the house. Especially since, as you say, you are in a cold climate, which means that it's very likely that in plenty of places around the house, you have cold walls and windows that will condense the increased humidity you're adding to the environment in the house.
One detail missing from your post is how it is that this one bedroom has "very low humidity" while the rest of the house seems fine. Humidity (relative) is simply a function of the temperature and the moisture content of the air. Typically, the moisture content in an enclosed building is going to mix well enough that the absolute humidity is the same everywhere, so the only other factor would be temperature. Are you keeping that one room significantly warmer than the rest of the house somehow? Given that the door can't be closed, how is that happening?
Unless the rest of the house has been set up as a greenhouse or something, it's hard to see how you could have one room having significantly different humidity from the rest of the house (and even then, with the open door it's still a puzzler). You might want to revisit your conclusion that the only place you need to address humidity is in that one room. Maybe what you really need is a whole-house humidifier.
Beyond that, I'd have to say I'm very skeptical of the proposal to pipe humid air in from a different room. Taking your statements at face value, that seems like it would only add way too much humidity elsewhere, causing other problems.
Comments are emphemeral, but you've provided important clarification in comments below, so I will copy them and my responses here:
The rest of the house is also low humidity. The other bedrooms are addressed with single room humidifiers as those doors are closed at night.
The house has two furnaces. We got an Aprilaire "whole house" unit installed on one of the zones (in the basement, which had convenient water/didn't require all the special sauce to prevent the water from freezing) and frankly I haven't been able to tell the difference (I still zap everything as I walk around, etc.). So I wasn't thrilled about paying a ton more money to get a second one in the attic.
"I haven't been able to tell the difference " — part and parcel of addressing any humidity issue is to make sure you measure the humidity. In a cold climate in the winter, you may still get static even with increased humidity. Conversely, by measuring, you can make sure your humidification system is adding sufficient moisture to the air, and set it accordingly.
"I wasn't thrilled about paying a ton more money to get a second one in the attic" — Understood. But sufficient system-wide humidification can be less cost in the long run. Fact is, your "humidifier in the other room" idea is essentially a system-wide humidification system anyway, because you anticipate losing a significant amount of moisture to the rest of the house. I.e. that humidifier is going to humidify the entire house, just not in the controlled way you'd like, thus risk additional expenditures (and at the very least, hassles) dealing with the problems (like condensation and mold).
In other words, given all the information provided, I still am of the opinion that the proposed system is likely to give you trouble, and a whole-house (or at least whole-zone) system will actually work better and cost less in the long run.